If q is a member of the set {21, 22, 24, 25, 26, 27} what is the value of q?
(1) q has exactly 1 prime factor
(2) q is divisible by 3
The OA is C.
I don't know how to prove that the correct answer is the option C. I believe is E. May someone clarifies this for me?
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If q is a member of the set {21, 22, 24, 25, 26, 27}
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GMATGuruNY
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Statement 1:VJesus12 wrote:If q is a member of the set {21, 22, 24, 25, 26, 27} what is the value of q?
(1) q has exactly 1 prime factor
(2) q is divisible by 3
Here, there are exactly two options for q:
Case 1: q=25, since the only prime factor of 25 is 5.
Case 2: q=27, since the only prime factor of 27 is 3.
Since q can be different values, INSUFFICIENT.
Statement 2:
Here, there are exactly two options for q:
Case 2: q=27, since 27 is divisible by 3.
Case 3 and 4: q=21 or q=24, since both values are divisible by 3.
Since q can be different values, INSUFFICIENT.
Statements combined:
Both statements are satisfied only by Case 2.
In Case 2, q=27.
SUFFICIENT.
The correct answer is C.
Last edited by GMATGuruNY on Wed Apr 18, 2018 7:30 am, edited 1 time in total.
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Hi Vjesus12.
I would solve this question as follows:
Let's call A={21, 22, 24, 25, 26, 27}. The prime factorization of the elements of A are:
21 = 3*7
22 = 2*11
24 = 2*2*2*3
25 = 5*5
26 = 2*13
27 = 3*3*3
(1) q has exactly 1 prime factor
Watching the list, we can see that there are two options for q : 25 and 27. Hence, this statement is NOT SUFFICIENT.
(2) q is divisible by 3
Again, there are 3 different options for q : 21, 24 and 27. Hence, this statement is NOT SUFFICIENT.
Using both statements together
The unique number that is in the statement (1) and also is in the statement (2) is q=27. Hence, both statements together are SUFFICIENT.
I hope this answer may help you.
I would solve this question as follows:
Let's call A={21, 22, 24, 25, 26, 27}. The prime factorization of the elements of A are:
21 = 3*7
22 = 2*11
24 = 2*2*2*3
25 = 5*5
26 = 2*13
27 = 3*3*3
(1) q has exactly 1 prime factor
Watching the list, we can see that there are two options for q : 25 and 27. Hence, this statement is NOT SUFFICIENT.
(2) q is divisible by 3
Again, there are 3 different options for q : 21, 24 and 27. Hence, this statement is NOT SUFFICIENT.
Using both statements together
The unique number that is in the statement (1) and also is in the statement (2) is q=27. Hence, both statements together are SUFFICIENT.
I hope this answer may help you.
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Jeff@TargetTestPrep
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We need to determine the value of q given that q is a member of the set {21, 22, 24, 25, 26, 27}.VJesus12 wrote:If q is a member of the set {21, 22, 24, 25, 26, 27} what is the value of q?
(1) q has exactly 1 prime factor
(2) q is divisible by 3
Statement One Alone:
q has exactly 1 prime factor.
If that is the case, the q is either a prime or a power of a prime. We see that none of the integers in the set is prime, however, both 25 and 27 are a power of a prime (25 = 5^2 and 27 = 3^3). Since q can be either 25 or 27, statement one alone is not sufficient.
Statement Two Alone:
q is divisible by 3.
We see that 21, 24, and 27 are divisible by 3, so q can be any one of these integers. Statement two alone is not sufficient.
Statements One and Two Together:
Using statements one and two, we see that q must be 27.
Answer: C
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